Both Spain and Italy appear unwilling to accept a new group of 141 migrants rescued by the Aquarius boat on Friday.
MSF and SOS MEDITERRANEE remain extremely concerned about European policies that hinder the provision of humanitarian assistance and which have resulted in a great;y increased number of deaths at sea in recent months.
Spokeswoman Tove Ernst said: "It could of course be the case that in theory a flag state of a rescue ship could be considered a potential location for disembarkation, but this might not be possible in practice".
Italy's transport minister has said the United Kingdom should take in 141 migrants picked up by a rescue ship that sails under the flag of the British territory of Gibraltar.
A total of 141 people were rescued on Friday by the search and rescue vessel Aquarius, chartered by SOS MEDITERRANEE and operated in partnership with Médecins Sans Frontières (MSF).
All migrants were eventually rescued by a patrol vessel. The other 116 migrants, 67 of whom are unaccompanied minors, were picked up in a separate operation.
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"It can go where it wants, not in Italy!" far-right Interior Minister Matteo Salvini said, while mentioning France, Germany, Britain or Malta as destinations for the ship.
When asked why the ship had not made for Libya, the nearest port at the time of rescue, Beau said that, according to worldwide law: "A safe port is a port in which people can obtain protection, which is absolutely not the case in Libya in the current situation".
More than 650,000 migrants have come to Italy's shores since 2014, and Rome has accused its European Union peers of not sharing the burden of taking in those who arrive on the bloc's southern border.
"What is of utmost importance is that the survivors are brought to a place of safety without delay, where their basic needs can be met and where they can be protected from abuse", said Nick Romaniuk, search and rescue coordinator for SOS Mediterranee. On Sunday the nation's coast guard said it rescued 60 Europe-bound migrants, including women and children, off the Mediterranean coast.
Image: Italy and Malta have stopped the Aquarius docking.
Though departures from Libya have fallen dramatically this year, people smugglers are still pushing some boats out to sea and an estimated 720 people died in June and July when charity ships were mainly absent, Amnesty International estimates.
"Policies created to prevent people from reaching Europe at all costs are resulting in more suffering and forcing those who are already vulnerable to take even riskier journeys to safety".